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Quasi point-symmetry models based on \(f\)-divergence and decomposition of point-symmetry for multi-way contingency tables. (English) Zbl 1448.62085

Summary: For two-way contingency tables, the last author [Biom. J. 27, 895–905 (1985; Zbl 0579.62037)] considered the quasi point-symmetry (QP) model and the marginal point-symmetry (MP) model, and gave the theorem that the point-symmetry (PS) model holds if and only if both the QP and MP models hold. K. Tahata and S. Tomizawa [AStA, Adv. Stat. Anal. 92, No. 3, 255–269 (2008; Zbl 1477.62148)] provided similar theorems for multi-way tables. For multi-way tables, the present paper proposes the quasi point-symmetry (QP[\(f\)]) model based on \(f\)-divergence. The QP[\(f\)] model includes the QP model in a special case. It also gives the theorem that the PS model holds if and only if both the QP[\(f\)] and MP models hold, and the theorem that the test statistic for goodness-of-fit of the PS model is asymptotically equivalent to the sum of those for the decomposed models under the PS model.

MSC:

62H17 Contingency tables
62B05 Sufficient statistics and fields
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